why dont use already existing date modules Eg:- Date::Calc For instance the code can be simplified to

use strict;
use warnings;
use Date::Calc qw(Today Add_Delta_Days);

my $today = sprintf("%02d%02d%02d",Today());

my $year = 1986;
my $month = 1;
my $day = 1;
my $offset =0 ;
my $print_date = 0;

while ($today > $print_date){
        my ($new_year,$new_month,$new_day)= Add_Delta_Days($year,$month,$day, $offset);
        $print_date =  sprintf("%02d%02d%02d",$new_year,$new_month,$new_day);
        print "$print_date\n";
        $offset++;
}

Depending on your req you can alter where ever needed
Cheers